In classical mechanics, the constants of motion of an isolated system are energy, linear momentum, and angular momentum. So far in this book, angular momentum has not been considered. This chapter starts by defining classical angular momentum and then proceeds to find the corresponding quantum operators. Following this, a hydrogenic atom is studied as a prototype application.

The Hamiltonian for $N$ particles subject to mutual two-body interactions

Engineers who design transistors, lasers, and other semiconductor components want to understand and control the cause of resistance to current flow so that they may better optimize device performance. A detailed microscopic understanding of electron motion from one part of a semiconductor to another requires the explicit calculation of electron scattering probability. One would like to know how to predict electron scattering from one state to another – something quantum mechanics can do.

In this chapter, we focus on post-training backdoor defense for classification problems involving only a few classes, particularly just two classes (K = 2), and involving arbitrary numbers of backdoor attacks, including different backdoor patterns with the same source and/or target classes. In Chapter 6, null models were estimated using (K – 1)2 statistics. For K = 2, only one such statistic is available, which is insufficient for estimating a null density model. Thus, the detection inference approach cannot be directly applied in the two-class case. Other detection statistics, such as the median absolute deviation (MAD) statistic used by Neural Cleanse, are also unsuitable for the two-class case. The developed method relies on high transferability of putative backdoor patterns that are estimated sample-wise, that is, a perturbation specifically designed to cause one sample to be misclassified also induces other (neighboring) samples to be misclassified. Intriguingly, the proposed method works effectively with a common (theoretically derived) detection threshold, irrespective of the classification domain and the particular attack. This is significant, as it may be difficult to set the detection threshold for any method in practice. The proposed method can be applied for various attack embedding functions (additive, patch, multiplicative, etc.).

In previous chapters, we saw in detail the immense success of quantum theory in describing microscopic systems. We also saw that it leads to concrete predictions that are persistently being confirmed by experiment, even predictions that grossly violate all physical intuition that had been generated by 250 years of classical physics.

This chapter introduces the cartographic approach to syntax, analysing the clause periphery. Module 4.1 argues that a complementiser like that is the head of a FORCEP/force projection marking declarative force, and peripheral topics (whether dislocated, fronted, or orphaned) are specifiers of lower TOPP/topic projections. Module 4.2 goes on to argue that peripheral focused constituents move from an initial position below the periphery to the edge of a peripheral FOCP/focus projection, and contrasts topic and focus. Module 4.3 then argues that peripheral clausal modifiers are directly generated on the edge of a MODP/modifier projection, and that (non)finiteness markers (like infinitival for) are generated as heads of a FINP/finiteness projection which is the lowest projection in the periphery. Next Module 4.4 contrasts complete clauses which project all the way up to FORCEP with truncated clauses which project only as far as FINP. The chapter concludes with a Summary (Module 4.5), Bibliography (Module 4.6), and Workbook (Module 4.7), with some Workbook exercise examples designed for self-study, and others for assignments/seminar discussion.

Chapter 5 extends the cartographic analysis of the clause periphery. Module 5.1 analyses Negative/Interrogative Inversion as involving a focused negative/interrogative XP moving through spec-FINP (concomitantly attracting an auxiliary to move to FIN) before moving to spec-FOCP. Module 5.2 goes on to look at embedded wh-questions (arguing that these involve a wh-XP moving to spec-FORCEP), and at how come questions (taking these to involve how come directly generated in spec-FORCEP). Module 5.3 then analyses yes-no questions, arguing that these involve an abstract yes-no question operator which behaves similarly to wh-question operators. Module 5.4 examines exclamative clauses (taking these to involve movement of an exclamative wh-XP to spec-FORCEP), and standard and non-standard relative clauses, analysing these as involving an overt/null relative operator on the edge of a RELP/relative projection positioned above a declarative/interrogative/exclamative/imperative FORCEP. The chapter concludes with a Summary (Module 5.5), Bibliography (Module 5.6), and Workbook (Module 5.7), with some Workbook exercise examples designed for self-study, and others for assignments/seminar discussion.

This chapter explores central questions of relationship dissolution: Why and how do people voluntarily breakup? What are the consequences of a close relationship ending? How do people recover and move on from difficult relationship endings? It begins with a discussion of the typical precursors of relationship dissolution, including problems with “me” or “you” (e.g., personality traits, attachment orientation, difficult habits), problems with “us” (e.g., romantic disengagement, disillusionment, incompatibility, infidelity), and problems in the context (e.g., financial stress, incarceration, parenting challenges). Then, it reviews the process of breaking up, including strategies people use to end their relationships. Finally, this chapter ends with a summary of the common immediate negative consequences of relationship dissolution and the common long-term recovery process (as well as diverse post-dissolution outcomes).

Newtonian mechanics was the first great synthesis of modern physics. It provided the main theory about the workings of the physical world from the date of its first presentation (1687) until the beginnings of the twentieth century.

The study of composite systems typically requires their analysis into simpler systems. In classical physics, the simplest systems are particles, that is, pointlike bodies that move in space. A particle is traditionally described by three position coordinates and three momenta, so the associated state space is ${ℝ}^6$. In Chapter 14, we will see that this description is incomplete: Particles also have an additional degree of freedom called spin.

This chapter introduces relationship initiation, the process by which people come to mutually identify themselves as in a romantic relationship. The chapter first describes how relationship readiness, romantic motives, and sociosexuality affect relationship initiation. Then, the chapter outlines the strategies and tactics that facilitate initiation (e.g., conspicuous consumption, altruistic acts), the gender roles that influence which strategies people use, and the major barriers that hinder relationship initiation (e.g., access to partners, shyness, low self-esteem). The chapter also reviews the stages that often occur as relationships develop, as well as divergent initiation paths. Lastly, the chapter covers the surprisingly influential role that other people play in shaping initiation trajectories and the reasons why most “could-be” relationships do not become relationships (e.g., rejection, ineffective initiation approaches).

In classical mechanics, a particle of mass $m$ subject to a restoring force linear in displacement, $x$, from a potential minimum such that $F(x)=-{\kappa }_{0}x$, where ${\kappa }_0$ is the force constant, results in one-dimensional simple harmonic motion with an oscillation frequency $\omega =\sqrt{{\kappa }_0/m}$.

The fundamental kinematical symmetry is the invariance under transformations between inertial reference frames. In the regime of small velocities, this symmetry corresponds to the Galilei group. However, the Galilei symmetry is only approximate. The exact symmetry, in the absence of gravity, is defined by the Poincaré group, which we analyse here.